A linear regression line is of the form w 1x+w 2=y and it is the line that minimizes the sum of the squares of the distance from each data point to the line. So, given n pairs of data (x i, y i), the parameters that we are looking for are w 1 and w 2 which minimize the error
and we can compute the parameter vector w = (w 1 , w 2) T as the least-squares solution of the following over-determined system
Let's use numpy to compute the regression line:
from numpy import arange,array,ones,random,linalg from pylab import plot,show xi = arange(0,9) A = array([ xi, ones(9)]) # linearly generated sequence y = [19, 20, 20.5, 21.5, 22, 23, 23, 25.5, 24] w = linalg.lstsq(A.T,y) # obtaining the parameters # plotting the line line = w*xi+w # regression line plot(xi,line,'r-',xi,y,'o') show()We can see the result in the plot below.
You can find more about data fitting using numpy in the following posts: